∗-Autonomous categories, revisited

∗-autonomous categories, revisited

functionals as A and one the greatest such topology. We assume without further mention that in any extensional object (V, V ′) of Chuse , V ′ can be assumed to be a set of functionals. Also in any map (f, f ′): (V, V ′) −→ (W,W ′), f ′ = − ◦ f . Let A denote the space with the same underlying vector space as A and in which a linear subspace U ⊆ A is open when every functional on |A| that vanish...

Topological ∗-autonomous categories, revisited

Given an additive equational category with a closed symmetric monoidal structure and a potential dualizing object, we find sufficient conditions that the category of topological objects over that category has a good notion of full subcategories of strong and weakly topologized objects and show that each is equivalent to the chu category of the original category with respect to the dualizing obj...

Continuous Categories Revisited

Generalizing the fact that Scott’s continuous lattices form the equational hull of the class of all algebraic lattices, we describe an equational hull of LFP, the category of locally finitely presentable categories, over CAT. Up to a set-theoretical hypothesis this hull is formed by the category of all precontinuous categories, i.e., categories in which limits and filtered colimits distribute. ...

Nonsymmetric *-Autonomous Categories

Compactification of *-autonomous categories

We study the question when a ∗-autonomous (Mix-)category has a representation as a ∗-autonomous category of a compact one. We prove that necessary and sufficient condition is that weak distributivity maps are monic (or, equivalently epic). For a Mix-category, this condition is, in turn, equivalent to the requirement that Mix-maps be monic (or epic). We call categories satisfying this property t...